CA Foundation · Quantitative Aptitude · Index Numbers
A price index series with base 2015 = 100 reads 150 for 2020 and 240 for 2024. The series is to be spliced to a new series with base 2020 = 100. What would be the 2024 index on the new base 2020 = 100, and what does it mean?
The 2024 index on base 2020 = 100 is 160, found as 240 divided by 150 times 100. This means prices in 2024 were 60% higher than in 2020. Shifting the base requires dividing by the new base year's old index.
- A90, meaning prices fell by 10% from 2020 to 2024
- B160, meaning prices rose by 60% from 2020 to 2024Correct
- C140, meaning prices rose by 40% from 2020 to 2024
- D360, meaning prices rose by 260% from 2020 to 2024
Explanation
New index for 2024 = 240/150 × 100 = 160. So prices in 2024 are 160% of 2020 prices, a rise of 60%. The option 90 comes from subtracting 150 from 240 and not dividing. The option 360 comes from multiplying 240 × 150/100, a wrong base shift.
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